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Number of relations on a small set that are reflexive, symmetric or equivalence

This type of question, asked 3 times: 30 Jan 2024, 22 Jan 2025, 21 Jan 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    30 Jan 2024

    177
    The number of symmetric relations defined on the set {1,2,3,4}\mathbf{\{ 1,2,3,4\}} which are not reflexive is

  2. Question 2

    22 Jan 2025

    51
    The number of non-empty equivalence relations on the set {1,2,3}\mathbf{\{ 1,2,3\}} is :

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  3. Question 3

    21 Jan 2026 S1

    53
    The number of relations, defined on the set {a,b,c,d}\mathbf{\{ a,b,c,d\}}, which are both reflexive and symmetric, is equal to:

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